I highly recommend that people try Lux since she is free. She is my favorite champion of all time.
I build her as a straight AP caster and focus on using positioning and exploiting her range to keep myself alive. Buy a morellos, Ionian boots, and a deathcap. You can also get an archangels if you are particularly spammy feeling.
Start with whatever you like. I tend to start with a Dorans Ring, but you can also go Boots+3 or Meki Pendant.
Lux is a Mage, not a support. Don't let anyone tell you otherwise. You need CS.
R > E > Q > W, starting with Q. Getting W (shield) at 4 is optional, and a decision I am not yet sure on. If you are solo go without, get it if you are duo laning.
9/0/21, Flash/CV. Flash for "oops" moments and lane aggressiveness, CV for spotting laser targets Nd general map control (your team will love you for taking CV).
For the record, my runes are MPen/ScalingMP5/CDR/HP. These are not particularly important. Any Mage page will work (hah, that rhymes).
Leverage your E plus your passive to get last hits and harass in lane. Ignore your passive after the laning phase. You should not be autoattacking in teamfights. If you are, you are too close.
When teamfighting, stick to the edges of the fight and use your long range. Dont forget to throw your shield in as well.
There is one inevitable question for new Lux's: When to fire her laser.
A) Before a teamfight starts if you catch them grouped up.
B) During a teamfight.
C) After a teamfight to pick off survivors.
The correct answer is D: all of the above, in the same teamfight. With max CDR Lux's ult is on a 24 second cooldown. Never hesitate to use it.
Note: Whenever I tell someone to build Morello's (or do it myself), SOMEONE complains that DFG is so much better that I should always pick it up over Morello's. This may be true on most champs, but on Lux it is not. The range on DFG is short. If you are close enough to use DFG as Lux you are far too close.